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Information Rates Over Multi-View Channels

V. Arvind Rameshwar, Nir Weinberger

TL;DR

This work analyzes information rates when a transmitted symbol yields $d$ independent noisy views through a multi-view channel. It proves that the mutual information $I^{(d)}$ and the dispersion $\mathsf{V}^{(d)}$ converge exponentially fast in $d$ to the input entropy $\mathsf{H}(X)$ and varentropy $\mathsf{V}(X)$, with a rate $\rho=\min_{x\neq x'}\mathsf{C}(P_{Y|x},P_{Y|x'})$ determined by the smallest Chernoff information between conditional output laws; this result extends from single-letter DMCs to multi-letter channels and provides explicit bounds for deletion channels. The paper also introduces the Poisson approximation channel $\mathsf{Poi}_d(p)$, showing its capacity tightly lower-bounds the multi-view Binomial channel and offering practical non-asymptotic insight for finite $d$. Together, these findings illuminate finite-blocklength performance and guide design considerations for complex sensing-storage systems such as DNA-based storage, where multiple reads of short sequences inform reliable decoding. The methods combine large-deviation theory, Chernoff bounds, and information-density analyses to link multi-view capacity to fundamental input statistics.

Abstract

We investigate the fundamental limits of reliable communication over multi-view channels, in which the channel output is comprised of a large number of independent noisy views of a transmitted symbol. We consider first the setting of multi-view discrete memoryless channels and then extend our results to general multi-view channels (using multi-letter formulas). We argue that the channel capacity and dispersion of such multi-view channels converge exponentially fast in the number of views to the entropy and varentropy of the input distribution, respectively. We identify the exact rate of convergence as the smallest Chernoff information between two conditional distributions of the output, conditioned on unequal inputs. For the special case of the deletion channel, we compute upper bounds on this Chernoff information. Finally, we present a new channel model we term the Poisson approximation channel -- of possible independent interest -- whose capacity closely approximates the capacity of the multi-view binary symmetric channel for any fixed number of views.

Information Rates Over Multi-View Channels

TL;DR

This work analyzes information rates when a transmitted symbol yields independent noisy views through a multi-view channel. It proves that the mutual information and the dispersion converge exponentially fast in to the input entropy and varentropy , with a rate determined by the smallest Chernoff information between conditional output laws; this result extends from single-letter DMCs to multi-letter channels and provides explicit bounds for deletion channels. The paper also introduces the Poisson approximation channel , showing its capacity tightly lower-bounds the multi-view Binomial channel and offering practical non-asymptotic insight for finite . Together, these findings illuminate finite-blocklength performance and guide design considerations for complex sensing-storage systems such as DNA-based storage, where multiple reads of short sequences inform reliable decoding. The methods combine large-deviation theory, Chernoff bounds, and information-density analyses to link multi-view capacity to fundamental input statistics.

Abstract

We investigate the fundamental limits of reliable communication over multi-view channels, in which the channel output is comprised of a large number of independent noisy views of a transmitted symbol. We consider first the setting of multi-view discrete memoryless channels and then extend our results to general multi-view channels (using multi-letter formulas). We argue that the channel capacity and dispersion of such multi-view channels converge exponentially fast in the number of views to the entropy and varentropy of the input distribution, respectively. We identify the exact rate of convergence as the smallest Chernoff information between two conditional distributions of the output, conditioned on unequal inputs. For the special case of the deletion channel, we compute upper bounds on this Chernoff information. Finally, we present a new channel model we term the Poisson approximation channel -- of possible independent interest -- whose capacity closely approximates the capacity of the multi-view binary symmetric channel for any fixed number of views.
Paper Structure (12 sections, 18 theorems, 166 equations, 1 figure)

This paper contains 12 sections, 18 theorems, 166 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Notation Conventions
  3. Main Results for DMCs
  4. Proof Sketch of Main Results
  5. Convergence of Mutual Information for BIMS Channels
  6. Convergence for Multi-Letter Channels and Some Examples
  7. Upper Bounds on $\rho_n$ for the Deletion Channel
  8. Poisson Approximation Channel
  9. Proofs
  10. Convergence of Mutual Information for General DMCs
  11. Convergence of Channel Dispersion of DMCs
  12. Conclusion and Future Work

Key Result

Theorem 3.1

We have that and where

Figures (1)

  • Figure 1: Plots comparing $C(\mathsf{Bin}(p))$ and $C(\mathsf{Poi}(p))$ for $p\in [0,1]$, and $d\in \{3,6,12,24\}$.

Theorems & Definitions (37)

  • Theorem 3.1
  • Theorem 3.2
  • proof
  • Theorem 3.3
  • Lemma 4.1
  • Corollary 4.1
  • proof
  • Lemma 4.2
  • proof
  • proof : Proof of Thm. \ref{['thm:conv']} for BIMS channels with uniform inputs
  • ...and 27 more